Hodge-Riemann Relations for Schur Classes in the Linear and K\"ahler Cases

TL;DR

This paper establishes Hodge-Riemann bilinear relations for Schur polynomials of K"ahler and positive forms, extending classical geometric inequalities to algebraic and complex vector space contexts.

Contribution

It introduces a novel version of Hodge-Riemann relations applicable to Schur polynomials of K"ahler and positive forms, broadening the scope of classical Hodge theory.

Findings

Proves Hodge-Riemann relations for Schur polynomials of K"ahler forms.

Extends Hodge-Riemann relations to Schur polynomials of positive forms.

Provides new algebraic inequalities in complex geometry.

Abstract

We prove a version of the Hodge-Riemann bilinear relations for Schur polynomials of K\"ahler forms and for Schur polynomials of positive forms on a complex vector space.